This talk focuses on a classical growing process, called multi-particle diffusion-limited aggregation (MDLA), where growth is governed by the aggregation of moving particles.
This model was introduced in the physics literature in 1980 with the goal of providing an example of “a simple and tractable” mathematical model of dendritic growth, which (similar to what has been observed in nature) produces a delicate, fractal-like geometry. Almost four decades later we still encounter tremendous mathematical challenges studying its geometric and dynamic properties, and understanding the driving mechanism lying behind the formation of fractal-like structures. In this talk, I will survey the developments in this field, giving emphasis to a new process, based on the competition of two growing systems, which we introduce and use to better understand MDLA. This is based on joint works with Elisabetta Candellero and Vladas Sidoravicius.